Answer to Question #212826 in Electricity and Magnetism for NICKO

Question #212826

(a)Derive an expression for VA − VB, the potential difference between points A and B (b) Does your result reduce to the expected answer when d = 0? When a = 0? and when q = 0.


1
Expert's answer
2021-07-04T17:45:39-0400

VA=kQrA,VB=kQrBV_A=\frac{kQ}{r_A},V_B=\frac{kQ}{r_B}


VAVB=kQrAkQrB=kQ(1rA1rB)V_A-V_B=\frac{kQ}{r_A}-\frac{kQ}{r_B}={kQ}({\frac{1}{r_A}-\frac{1}{r_B}})

VAVB=kQrBrArArBV_A-V_B=kQ\frac{r_B-r_A}{r_Ar_B}

When

d=rBrA=0;q=Q=0;a=rA=0d=r_B-r_A=0;q=Q=0;a=r_A=0

Put value then We can written as

VBVA=0V_B-V_A=0

VA=VBV_A=V_B


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